Potential flow, also know as incompressible flow or irrotational flow in fluid mechanics is flow defined by the equations

(zero rotation = no viscosity)

(zero divergence = volume conservation)

Equivalently,

where:

v is the vector fluid velocity
Φ is the fluid flow potential, scalar
" ×" is curl
" ·" is divergence

Together with the Navier-Stokes equations and the Euler equations, these equations can be used to calculate solutions to many practical flow situations. In two dimensions, potential flow reduces to a very simple system that is analysed using complex numbers.

Unfortunately, potential flow bears very little resemblance to many flows that are encountered in the real world. For example, potential flow excludes turbulence, which is commonly encountered in nature. Richard Feynmann considered potential flow to be so unphysical that the only fluid to obey the assumptions was "dry water".

Potential flow also makes a number of predictions, such as d'Alembert's paradox, which states that the drag on any object moving through an infinite fluid otherwise at rest is zero.

More precisely, potential flow cannot account for the behaviour of flows that include a boundary layer. Someone once said that flows are split into those that are observed but never calculated, and those that are calculated but never observed.

Nevertheless, understanding potential flow is important in many branches of fluid mechanics. In particular, simple potential flows such as the free vortex and the point source possess ready analytical solutions. These flows correspond closely to real-life flows over the whole of fluid mechanics; in addition, many valuable insights arise when considering the deviation (often slight) between an observed flow and the corresponding potential flow.